Some people have had over 1000. IIRC some over 2000... which is insane lol. It averages out to something like 5 hours a day IF you only spend a few seconds on each game.
Understandably some have started that many, and then quit half way though.
As far as I know the site doesn't prevent you from starting new games. Update browser, don't use IE, clear cache and all that I guess would be the first tips for fixing that error message you're getting.
So I've recently discovered the beauty of this daily chess after getting frustrated over bullet games. I play them every now and then, but I mostly play daily now. I love it.
However, I thought I was a boss by having 70 games going on at once, but now I've seen a person with 250 games going on at once, and I've read that some people have 300-500 going on at once.
How do you get that many games going? After a few clicks I get the "there was an error processing your request" which I assume is normal. But when I was at 70 games going on at once, it wouldn't let me start a new game, even days after I had tried to start a new one.
I want like 1000 games in 14 days going on...there's just something about not being able to catch up that I like...it motivates me.